Pi as a half-circle, once you start using graphs and trig makes a whole lot of sense.

I've read there's been recent discovery of a pile of Archimedes' writings. The man was on to the limit or working on it before the Roman soldier showed him who's boss.

There's an ancient Arabic proof of the Pythagorean Theorem from centuries before Pythagoras that I always liked because it's geometric. But my hat's off to the Indian scholars who invented zero and went on to other depths (finite series, maybe infinite series) maybe 1000 years before Newton.

I remember finding out why the volume of a sphere is 4/3 Pi R^3, why the 4/3. It doesn't "prove" anything but the volume of a sphere but it was nice to know how. Which brings me to this whole "proves" thing. Some people have awfully loose ideas about what proof is, ie: "I want" + "something convenient with no real connection" = "proof". Please.. just.. think.

There may exists algebraic proof of the volume of a sphere but if you do integral calculus, the volume is fairly easily found. What was hard for me in college was finding volume of n-dimensional sphere. I never got the concept right to start with.

One can find many things in strange places if one really wants to find it there. The tests and the results are easily manipulated to yield the desired result. And one can waste much time chasing after foolishness thinking one is wise because he believes the lies others are telling him. And some just think that they are so superior to other humans that they don't need anyone else's input to feel superior.

He who thinks himself wise should take care lest others see him as he really is. Kind of like the "Emperors New Clothes".